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The Hubble tension casts a blight on the standard cosmology. As a possiblesolution to the problem, the local variation of the expansion rate has beenproposed where the spatial averaging over a finite domain was introduced inorder to restore the local Friedmannian behavior in an inhomogeneous cosmology.So far, however, the approaches are limited to the particular choices of thegauges, and it has been unclear whether the results are gauge-invariant. Inthis paper, we present the gauge-invariant formulation of the local expansionrate which is driven by the spatial average of the gauge-invariantinhomogeneous density. We show that the local cosmological parameters in thefinite domain may change from the global parameters, and the relations betweenthem are expressed by the gauge-invariant averaged density.

The gauge-invariant formulation of the local expansion rate driven by the local average density in an inhomogeneous universe